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where g is an arbitrary function for growth rate. Throughout the article, subscripts are occasionally used to represent functions of a particular species (e.g. r j (t) is the fitness of species j). It is assumed that there must be some values e* and c*, such that g(e*, c*) = 0, representing a zero-population growth equilibrium.
The peacock tail in flight, the classic example of an ornament assumed to be a Fisherian runaway. Fisherian runaway or runaway selection is a sexual selection mechanism proposed by the mathematical biologist Ronald Fisher in the early 20th century, to account for the evolution of ostentatious male ornamentation by persistent, directional female choice.
Also, certain non-continuous activation functions can be used to approximate a sigmoid function, which then allows the above theorem to apply to those functions. For example, the step function works. In particular, this shows that a perceptron network with a single infinitely wide hidden layer can approximate arbitrary functions.
The collective goal is to contribute excellent biology diagrams to the Commons and to corresponding Wikipedia articles. This is done as part of an Advanced Placement Biology course. The lead editor is Chris Packard. This project is inspired by the 2009 Wikipedia AP Biology Project. There are many basic and important diagrams missing from ...
The Stone–Weierstrass theorem generalizes the Weierstrass approximation theorem in two directions: instead of the real interval [a, b], an arbitrary compact Hausdorff space X is considered, and instead of the algebra of polynomial functions, a variety of other families of continuous functions on are shown to suffice, as is detailed below.
Automata theory is the study ... contain loops of arbitrary complexity. Structure theory deals with the ... using automata theory in biology include mollusk and pine ...
In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function δf.
The Wiener–Hopf method is a mathematical technique widely used in applied mathematics.It was initially developed by Norbert Wiener and Eberhard Hopf as a method to solve systems of integral equations, but has found wider use in solving two-dimensional partial differential equations with mixed boundary conditions on the same boundary.
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